Vibration propagation in frame structure

Abstract

We consider propagation of longitudinal and transverse sound waves along T-shaped concrete frame structures which are combinations of walls and ceilings. The formulation of Morse [J. Acoust. Soc. Am. 22, 219 (1950)] and Muskat et al. [Geophysics V, 115 (1940)] is followed throughout, though not in detail. For the horizontal part of the structure, the boundary condition of the vanishing of the normal components of stresses over the bounding surfaces is used. Both a plane longitudinal wave and a transverse wave when incident on a solid/vacuum interface produce both a reflected longitudinal wave and a reflected transverse wave. For propagation along the vertical part of the structure, we use the boundary conditions that both the displacements and the stresses at the solid/solid interface shall be continuous. Transmission coefficients are plotted as functions of the incident frequencies and the angles of incidence. They are compared with the theoretical works of Cremer [Acustica 3, 317 (1953)] and Arenberg [J. Acoust. Soc. Am. 20, 1 (1948)] because no previous experimental work has been done for this type of structure. Comparison shows reasonable agreement on the shape of transmission coefficient curves.